Split flap - upper and lower surfaces are separate, the lower surface operates like a plain flap, but the upper surface stays immobile or moves only slightly.
Fowler flap (Fairey-Youngman flap) - slides backwards before hinging downwards, thereby increasing both camber and chord, creating a larger wing surface better tuned for lower speeds.
Slotted flap - a slot (or gap) between the flap and the wing enables high pressure air from below the wing to re-energize the air blowing over the flap. This helps the airflow to stay attached to the flap, delaying the stall.
Blown Flaps - systems that blow engine air over the upper surface of the flap at certain angles to improve lift characteristics.
Slats are similar to flaps - they are on the leading edge of the wing.